Labels vs. Concepts

One of the problems in American Education, I've come to believe, is that people confuse labels and concepts--and, by extension, definitions with conceptual information.

Mistaking labels for concepts, they ssume that a child who doesn't know what a "number sentence" is doesn't understand the concept of number sentences, or that an autistic child who doesn't know what "because" means doesn't understand cause and effect.

Or they teach biological terms like "endoplasmic reticulum" as definitions to memorize ("the part of the cell that assembles proteins and sends them to the nuclear membrane") rather than as biological entities (an organ within the cell that uses its structure in particular ways to cooperate in particular ways with the rest of the cell).

Then, mistaking concepts for labels, they avoid having children memorize detailed, concept-rich networks of facts like those of the Philogenic Tree or the Periodic Table. ("Mere facts"--right up there with "mere calculation").

In short, concept/label confusion leads people to understimated children (especially children who are gifted and/or autistic) whose conceptual understanding exceeds their vocabulary, to teach rote meanings stripped of underlying concepts, and to avoid teaching concepts whose grounding in detailed factual information causes people to mistake them for mere labels.

Math problems of the week: 3rd grade Investigations vs. Singapore Math, final fractions problems

In Memoriam: Clara Claiborne Park

"One of the first personal accounts of autism, and still the best." Oliver Sacks' assessment of Clara Claiborne Park's The Siege is as true now as it was when he made it. Clara passed away on July 3rd, 43 years after publishing this classic memoir about her autistic daughter, Jessica Park (now an acclaimed painter), and 9 years after publishing its sequel, Exiting Nirvana.

Great works of literature on many levels, these books offer two special things to those connected with autism. One is a living, breathing character, in all her fascinating, maddeningly baffling autistic glory---something that autism memoirs rarely evoke. The other is a host of insights about the world of autism. Extremely observant, intelligent, and reflective, Clara showed, in her one-on-one work with Jessy; in her observations about Jessy's autistic traits, linguistic deficits, and cognitive strengths; and in her spot-on critiques of the autism therapy world, that a wise and good person, regardless of formal credentials, often has more to offer to those touched by autism, and those interested in autism, than many of the most highly trained experts. If you are among these autism-affiliated people and haven't yet read Clara's work, I strongly urge you to do so. My students have to--it's required reading for two of my courses.

For me, one of Clara's most memorable observations was Few people are wise and good, occurring at the end of a section of The Siege that described her various frustrations dealing with autism professionals. Having had some experiences that were eerily similar to Clara's, I was inspired, especially by the passages that culminated in Few people are wise and good, to write the one fan letter I've ever written.

Clara responded and we soon became pen pals. She was one of the last people with whom I regularly exchanged handwritten letters. She invited J and me to visit, and we did--a number of times over the years. Despite all of J's mischievousness, they--Clara and her wonderful husband, David, and Jessy, too--welcomed us into their home, appreciated J, shared their lives (and Jessy's art) with me, and engaged me in all sorts of mind-bending, mind-broadening conversations.

Few people are wise and good. Clara Park was among them. I will miss her on many occasions.

Preventing bullying: yet more justifications for cooperative learning

In her latest New York Times Op-Ed piece, Susan Engel and co-author Marlene Sandstrom, both of Williams College, discuss ways to reduce bullying in schools. Claiming that

a growing emphasis on standardized test scores as the primary measure of “successful” schools has crowded out what should be an essential criterion for well-educated students: a sense of responsibility for the well-being of others

Engel and Sandstrom argue that "educators need to make a profound commitment to turn schools into genuine communities." Besides ensuring that they and their students have "conversations about relationships every day," and that students know that "kindness and collaboration to be every bit as important as algebra and reading," teachers should

structure learning activities in which children are interdependent and can learn to view individual differences as unique sources of strength. It’s vital that every student, not just the few who sign up for special projects or afterschool activities, be involved in endeavors that draw them together.

In other words, besides having students get together to talk about relationships, teachers should also have students get together for academic tasks.

As justification for this, the authors tell us to

look at Norway, where the prevention of such incidents became a major emphasis of the school system after three teenage victims of bullying committed suicide in 1983. There, everyone gets involved — teachers, janitors and bus drivers are all trained to identify instances of bullying, and taught how to intervene. Teachers regularly talk to one another about how their students interact. Children in every grade participate in weekly classroom discussions about friendship and conflict. Parents are involved in the process from the beginning.

But what's egregiously missing from this Norwegian comparison is any mention of Norwegian school children working cooperatively on academic assignments.

The anecdotes I collected for my book strongly suggest that group learning environments, rather than preventing bullying, are often arenas for it. Bullying can be quite subtle and difficult to detect; teachers cannot supervise multiple groups simultaneously; unsocial and socially awkward children regularly report being teased and ignored as the social hierarchy of the playground creeps into the classroom's "cooperative groups"--whenever the teacher is out of earshot.

Meanwhile, those who never stray within earshot of children who are supposed to be working together, and who never try their own hands at creating cooperative learning groups within k12 classrooms, can happily write Op-Ed pieces about how wonderfully these groups promote social harmony so long as they are "properly implemented."

Math problems of the week: 5th grade Investigations vs. Singapore Math

Final 5th grade fractions unit problems (left or top: Investigations; right or bottom: Singapore Math):

(Investigations in Number, Data and Space Student Activity Book p. 68 of Unit 4, "What's That Portion?"; Primary Mathematics 5A, p. 96, Unit 4, "Multiply and Divide Fractions")

Drawing the right lessons about creativity

An article in Newsweek, excerpted on JoanneJacobs, discusses the creativity crisis in America and how schools can go about addressing it. Its recommendations, unfortunately, risk taking schools further down the unpromising garden path along which they've already been wandering for quite some time now.

According to Torrance’s Creativity Index, a measuring tool that has had a high success rate predicting which children will go on to become "entrepreneurs, inventors, college presidents, authors, doctors, diplomats, and software developers," creativity among American children has been declining since 1990.

"One likely culprit," explains the article, "is the number of hours kids now spend in front of the TV and playing videogames rather than engaging in creative activities. Another is the lack of creativity development in our schools."

The ingredients for creativity training, neuroscience research suggests, are tasks that combine left-brained "convergent" thinking (with its narrow, analytical associations) with right-brained "divergent" thinking (with its broad, long distance associations).

When you try to solve a problem, you begin by concentrating on obvious facts and familiar solutions, to see if the answer lies there. This is a mostly left-brain stage of attack. If the answer doesn’t come, the right and left hemispheres of the brain activate together. Neural networks on the right side scan remote memories that could be vaguely relevant. A wide range of distant information that is normally tuned out becomes available to the left hemisphere, which searches for unseen patterns, alternative meanings, and high-level abstractions.

Having glimpsed such a connection, the left brain must quickly lock in on it before it escapes. The attention system must radically reverse gears, going from defocused attention to extremely focused attention. In a flash, the brain pulls together these disparate shreds of thought and binds them into a new single idea that enters consciousness. This is the “aha!” moment of insight, often followed by a spark of pleasure as the brain recognizes the novelty of what it’s come up with.

Now the brain must evaluate the idea it just generated. Is it worth pursuing? Creativity requires constant shifting, blender pulses of both divergent thinking and convergent thinking, to combine new information with old and forgotten ideas. Highly creative people are very good at marshaling their brains into bilateral mode, and the more creative they are, the more they dual-activate.

Consistent with the idea that in creativity, the left brain is as important as the right, the article makes several observations:

*The age-old belief that the arts have a special claim to creativity is unfounded. When scholars gave creativity tasks to both engineering majors and music majors, their scores laid down on an identical spectrum, with the same high averages and standard deviations. Inside their brains, the same thing was happening—ideas were being generated and evaluated on the fly.

*Creativity isn’t about freedom from concrete facts. Rather, fact-finding and deep research are vital stages in the creative process. 

*From fourth grade on, creativity no longer occurs in a vacuum; researching and studying become an integral part of coming up with useful solutions.

*What’s common about successful [creativity training] programs is they alternate maximum divergent thinking with bouts of intense convergent thinking, through several stages. Real improvement doesn’t happen in a weekend workshop. But when applied to the everyday process of work or school, brain function improves.

All this meshes not only with the research, but (less importantly, of course) with what I've long suspected about creativity. Despite what popular education theory keeps claiming, it is enhanced, not stifled, by content knowledge. And it is limited neither to right-brain thinking, nor to right-brain people.

Unfortunately, however, those whose recommendations the Newsweek article reports, like countless others who make recommendations without visiting actual classrooms, aren't aware of this bias, and their suggestions include things that will only make it stronger.  Consider what else the article reports:

*The European Union designated 2009 as the European Year of Creativity and Innovation, holding conferences on the neuroscience of creativity, financing teacher training, and instituting problem-based learning programs—curricula driven by real-world inquiry—for both children and adults.

*In China there has been widespread education reform to extinguish the drill-and-kill teaching style. Instead, Chinese schools are also adopting a problem-based learning approach.

*Researchers say creativity should be taken out of the art room and put into homeroom.

While the real-world, problem-based inquiry project that the article describes appears to combine left- and right-brain thinking, it has students working in groups (something that isn't entailed by the above research), and too much resembles the projects that are already proliferating around our schools, too many of which are far too open-ended to foster the focused, left-brain thinking that creativity, it turns out, requires:

Working in small teams, the fifth graders first engaged in what creativity theorist Donald Treffinger describes as fact-finding. How does sound travel through materials? What materials reduce noise the most? Then, problem-finding—anticipating all potential pitfalls so their designs are more likely to work. Next, idea-finding: generate as many ideas as possible. Drapes, plants, or large kites hung from the ceiling would all baffle sound. Or, instead of reducing the sound, maybe mask it by playing the sound of a gentle waterfall? A proposal for double-paned glass evolved into an idea to fill the space between panes with water. Next, solution-finding: which ideas were the most effective, cheapest, and aesthetically pleasing? Fiberglass absorbed sound the best but wouldn’t be safe. Would an aquarium with fish be easier than water-filled panes?

So here's my prediction: our education experts will read this article and conclude that we need more, not fewer, assignments across the curriculum that ask students to Be colorful! Be creative!, and more, not fewer, open-ended, real-world, group projects.

All of which will fail to inspire creativity, it turns out, not just in our left-brained math and science buffs, but in students in general.

The logic of computer programming courses

An article in last week's Education Week reports that schools are falling behind in their computer science offerings at the same time that the demand for programmers has risen. Computer science advocates are now calling for more computer science offerings in public schools.

In the process, some are trying to clear up a major confusion that has many schools offering courses on Microsoft Windows, Power Point, and Adobe Photoshop instead of actual programming courses:

Proponents of computer-science education say a major hurdle is simply getting school officials and others to understand what the field is, and isn't.

"One of the biggest problems is schools confusing computer literacy with computer science," said Barbara J. Ericson, the director for computing outreach and a research scientist at the Georgia Institute of Technology, in Atlanta.

"A lot of places don't understand the difference," agreed Ms. Cuny of the NSF, which is providing grants to support a variety of programs and research undertakings on computer-science education. "They're not teaching kids how to be creators of technology—they're teaching them how to be users of technology."

Sounds a bit like the confusion between teaching science and teaching science appreciation, and it's nice to see that the computer science advocates, unlike many of the science advocates, understand the difference.

Some computer programming advocates are concerned that even when schools do teach programming, they leave out many of the more challenging concepts that the pioneering programmers of tomorrow need to master.   As GoogleMaster recently commented on JoanneJacobs:

Learning to *use* computers is easy. Learning to *design* computer hardware or to write software that handles edge cases properly and not just the “happy path” is difficult. Millennials think they’re smarter than the boomers and the boomers’ parents merely because they can use the technology. They forget that the boomers and the generations before them invented the technology that the millennials are using.

- Internet (ARPAnet): 1960s, created by a team at MIT who were born late in the Silent Generation.
- First email message: 1969, sent by a Boomer.
- First cell phone: 1973, invented by Martin Cooper, Silent Generation.
- World Wide Web, first HTTP communication, 1990, Tim Berners-Lee, a Boomer.

As for music recording and playback: the pulse-code modulation that makes it possible was patented in 1937 by a member of the Greatest Generation. The first digital speech transmission was in 1943; computerized digital recording was invented in 1957.

If we don’t provide the STEM grounding necessary to understand the technology already in existence (how and why it works, not how to use it), I don’t see how future generations will be able to invent anything of substance.

The popular programming language now is Java, and for many hard core programmers this language is simply too easy. For example, Joel Spolsky laments on his software blog that the introductory programming course at the University of Pennsylvania now uses Java instead of Scheme and ML. Unlike Java, Scheme and ML involve hard concepts like pointers and functional programming (including recursion).  These concepts, Spolsky writes, are "still important for some of the most exciting programming jobs":

Without pointers, for example, you'd never be able to work on the Linux kernel. You can't understand a line of code in Linux, or, indeed, any operating system, without really understanding pointers.

Without understanding functional programming, you can't invent MapReduce, the algorithm that makes Google so massively scalable. 

Beyond these specific benefits:

Pointers and recursion require a certain ability to reason, to think in abstractions, and, most importantly, to view a problem at several levels of abstraction simultaneously. And thus, the ability to understand pointers and recursion is directly correlated with the ability to be a great programmer.

In a comment on the last blog post I wrote addressing these concerns, Seth, who helped to teach Penn's introductory programming course, concurs with Spolsky:

What he says about pointers and recursion enforcing and testing a certain way of thinking is a very important point, in my opinion.

But what I found really disturbing from helping to teach that course was that it was possible, indeed universal, that the students who came from the best high schools and had the most experience had never been exposed (consciously) to problems of recursion. Why is it that e.g. the Towers of Hanoi problem has to wait until college to be taught? Students need to be hit with this when they're younger, before their brains start to rot.

I really wish that when people talk about the need for computer in schools, the focus would be not just on computers, but computers as a way to teach how to think about breaking up a problem. But I'm an old-fashioned fart, so I still think that one of the best preparations for programming is geometry, and the process of proving a theorem. I'm scared to ask if that is still taught in high schools.

As our problems of the week here have shown, Seth has good reason to be scared.  In connecting geometry proofs with computer programming, he raises an important point: is the American education establishment, with all its calls to teach "higher level thinking skills," no longer interested in logical reasoning?

Actually, anyone who has tried to reason logically with some of these education leaders already knows the answer to that one.

Is the world right-brained or left-brained, III

David Brooks, for one, thinks it should be more left-brained--at least when it comes to business.  (When it comes to education and Asperger's Syndrome, Brooks' bias is more right-brained).  In his July 12th New York Times Op-Ed piece, he divides the business world into princes and grinds. Guess which ones are left-brained.

The princes?

If you go to business conferences, you know that at lunch it is definitely better to be seated next to a prince than a grind. Princes, who can be male or female, are senior executives at major corporations.

They are almost always charming, smart and impressive. They’ve read interesting books. They’ve got well-rehearsed takes on the global situation. They can drop impressive names as they tell you about their visits to the White House, Moscow or Beijing. If you’re having lunch or dinner with a prince, you’re going to have a good time.

Or the grinds?

Grinds, on the other hand, tend to have started their own company or their own hedge fund. They’re often too awkward to work in a large organization and too intense to work for anybody but themselves.

Over lunch, they can be socially inert. You try to draw them out by probing for one or two subjects of interest to them. But as often as not, you find yourself playing conversational ping-pong with a master of the monosyllabic response.

Every once in a while you’ll run into one who can’t help but let you know how much smarter he is than you or anybody else in the room. Sitting at this lunch is about as pleasant for him as watching a cockroach crawl up his arm. He’d much rather be back working in front of his computer screen.

And guess which ones, according to Brooks, make better contributions to the economy.

The princes?

Since the princes are nicer and more impressive, it is easy to be seduced into the belief that they also are more trustworthy. This is false. During the last few years, for example, the princes at Citigroup, Bear Stearns, Goldman Sachs and Lehman Brothers behaved with incredible stupidity.

...The smooth operators at the big banks were playing with other people’s money, so they borrowed up to 30 times their investors’ capital. 

The social butterflies at the banks got swept up in the popular enthusiasms... The well-connected bankers knew they’d get bailed out if anything went wrong. 

Or the grinds?

The hedge fund loners often behaved with impressive restraint.

[They] usually had their own money in their fund, so they typically borrowed only one or two times their capital.

...[They] knew they were on their own and regarded their trades with paranoid anxiety.

In short:

In finance, as in other realms of business life, social polish doesn’t always go with capitalist success. Often it is the most narrow, intense, awkward people who start the best companies, employ the most people and create the most value.

And guess which group Brooks thinks is doing better under today's recovery?

Sadly, this recovery has been great for princes and horrible for grinds... The big companies are posting excellent earnings. They’re sitting on mountains of cash.

The aspiring grinds, meanwhile, are dead in the water. Small businesses are not growing. They are not hiring. They are struggling to stay alive. (Though my friend Paul Downs, a small business owner who blogs for the New York Times, thinks things are improving).

In short:

The princes can thrive while the government intervenes in the private sector. They’ve got the lobbyists and the connections. The grinds, needless to say, don’t... [They] try to stay far away and regard the interlocking network of corporate-government schmoozing with undisguised contempt.

But the problem has spread beyond the grinds.  Because "very few grinds are bringing new ideas to scale and hiring workers to enact their us-against-the-world schemes," we have "an economy that is inching toward recovery but that is not creating much in the way of new innovations and new jobs..."

Brook's solution?

For jobs to recover, the grinds have to recover... Maybe the real issue is how we are going to light a fire under the country’s loners, its contrarians and its narrow, ambitious outsiders.

An interesting idea, but is it the undersides of the grinds that need fire, or those of the princes?

Math problems of the week: 6th grade traditional math vs. Everyday Math

Two ways to sum up a chapter on fractions, decimals, and percents: 1. "Problems without Numbers," from Chapter I of Hamilton's Essentials of Arithmetic: Second Book (intended for students in the "sixth, seventh and eighth years"), p. 79

2. "Time to Reflect," from Unit 4 of the 6th grade Everyday Mathematics Student Math Journal Volume I, p. 161.

How to make autism a "tiny disability"

As I look back on J's past year, one thing that stands out to me is how minimal and inadequate his official autism-related therapies were. Our regional autism center no longer provides any therapy at all, limiting its services to evaluations (and even for these there's quite a long waiting list). So all of J's official therapies have happened at school. Here, OT has been minimal, and speech therapy is conducted by an itinerant generalist untrained in autism-specific language deficits. I asked for more; nothing happened; I have yet to sign our 9-month-old IEP. I could have spent more time fighting; instead I spent the time I had working with J myself.

A few months ago it looked like a new opportunity had opened up: the new Kinney Center for Autism Education and Support at nearby St. Joseph's University was offering a social skills group for adolescents with autism. We called up, there was an opening, we faxed over evaluations and went through an accelerated intake. They couldn't wait to meet J. But then they did. "He doesn't comply with directions," the psychologist told me after he interviewed J with my husband, "and so he doesn't meet the requirements of our social group. We need kids who will follow directions." He promised to let us know if some other program opened up that might be appropriate for J.

So my ears pricked up the other morning when I heard the following words on WHYY's Morning Edition:

The long hot days of summer can pose challenges for families of special needs children. Parents have to find activities or camps where their child feels safe, welcome, and continues to learn. A new camp at Saint Joseph's University is trying a unique approach. It's especially designed to accommodate children with autism and pairs them with their typical peers.

Gee, they didn't tell us about this program, I thinks to myself, as I continue listening:

Executive director Michelle Rowe says having a mixed group of kids means opportunities for learning. "What that does it it allows the kids with autism to learn from their typically developing peers. In translation, that means that children with autism can benefit from learning what kinds of things are expected socially at different ages."

...

"The kids can be in the pool and also be interacting with each other – we take them for five hours a day, we expose them to a lot of fun, but also, they can't help but learn in the process."

Sounds great, I says to myself. A great opportunity, as well, for typical kids to learn about autism and about how to interact with autistic peers. But then I hear more:

As excited campers chatter about their favorite activities, it is nearly impossible to determine which children have Autism, and which don't:

[Sounds of kids' voices.] "I like it all!! We go swimming every day, we go to the play ground most of the days." "I like talking with my friends, I like swimming, and I like snack time." "Playing basketball!"

This is the first year for the camp, and the kids with autism are in the majority, but Rowe hopes to have more of a 50 – 50 mix in the future. She says the concept is also beneficial for typical kids, who learn to feel comfortable around people with disabilities. 7 year-old Ian sums it up:

Ian: "Kids with autism just have a tiny disability, not like a big difference, we're all the same in a couple of ways."

Nearly impossible to tell which ones have autism?? Only a tiny disability??  Tell that to a parent of an autistic child. Or take a look at J, so capable, yet so mischievous that he would never be admitted to this camp. Of course, that's precisely what's going on.

Indeed, besides the fact that the Kinney people didn't tell us about Camp Kinney at the time they evaluated J, there are an number of clues here suggesting that they handpicked the autistic campers to be minimally disabled--at least in ways that would inconvenience the staff and disturb their non-autistic peers. Consider, for example, how easy it was for one of the college undergraduate counselors to diffuse a child's temper tantrum:

St. Joseph's Psychology major Amber Leyton says learning about behaviors and explosive temper tantrums associated with Autism in a classroom is one thing – dealing with them first hand is another. But Leyton had no problems diffusing a situation when a young camper had a meltdown because he couldn't spend time with a counselor named Drew:

Leyton: "At first, it was just waiting for him to level out a little bit, and it was explaining to him, over and over the situation: if you calm down, you can eat your lunch, you can go see Drew, over and over again, the schedule, what was going to happen, and what was expected of him."

What this program seems to be striving for, as much in its admissions policies as in its hoped-for outcomes, are individuals like John Dorfman:

These kinds of situations [as in Drew's tantrum] are familiar to counselor John Dorfman from first-hand experience – he has autism. He says he wants to inspire the campers with his own story:

"Anything is possible! When I was in 9th grade, everyone was skeptical that I was even going to make it to college, and here I am, going into my senior year helping the other kids, it's really a great thing."

So long as potential providers resist providing intensive therapy and opportunities for peer interactions to the many, many individuals with more severe or challenging forms of autism, everyone but the families of such children can remain in happy denial, congratulating themselves on how openly they welcome autistic kids into their worlds and how open-mindedly they appreciate what a tiny disability autism really is.

I emerge from these thoughts in time to hear the program's closing remark:

Michelle Rowe says they had to turn away applicants this year, but hope to expand the program next summer.

Isn't it pretty to think so?

Please visit an actual classroom before making recommendations, VI

In this latest case it's hard to say what's more shocking: that the "expert" in question thinks she's qualified to make recommendations about general classroom pedagogy, or that the publication in question has given her a forum for doing so.

The expert in question: Martha Nussbaam, a professor of Law and Ethics at the University of Chicago Law School.

The publication in question: The New Republic.

In a July 1st opinion piece entitled "The Ugly Models", Nussbaum criticizes American liberals, specifically President Obama and New York Times columnist Nicholas Kristov, for extolling the virtues and successes of the Chinese and Singaporean education systems.

Alluding to "the Chinese government’s ferocious opposition to political dissent," Nussbaum writes:

Obama and Kristof and all the other U.S. proponents of Singapore and China’s educational systems apparently aren’t thinking very hard about the relationship of those policies to democratic debate and democratic autonomy. Indeed, they are glorifying that which does not deserve praise.

Nussbaum offers just one reason why these education systems don't deserve praise:

By their own internal accounts, [educators in China and Singapore] do a great deal of rote learning [sic] and “teaching to the test.”

Given that educators in the US have been making the same claims about US education from time immemorial, this presumably qualifies us as steadfast "Ugly Models" as well. But Nussbaum doesn't go there.

Instead, she implicitly concedes that there is a bright side to this Sino-Singaporean critical self-awareness, namely, an inkling of possible reform:

In recent years, both nations have conducted major educational reforms, concluding that a successful economy requires nourishing analytical abilities, active problem-solving, and the imagination required for innovation. In other words, neither country has adopted a broader conception of education's goal, but both have realized that even that narrow goal of economic enrichment is not well served by a system focused on rote learning.

Nussbaum elaborates Singapore's reform attempts in particular:

Singapore, similarly, reformed its education policy in 2003 and 2004, allegedly moving away from rote learning toward a more “child-centered” approach in which children are understood as “proactive agents.” Rejecting “repetitious exercises and worksheets,” the reformed curriculum conceives of teachers as “co-learners with their students, instead of providers of solutions.” It emphasizes both analytical ability and “aesthetics and creative expression, environmental awareness … and self and social awareness.”

The problem, Nussbaum explains, is that these reforms remain theoretical:

Observers of current practices in both Singapore and China conclude that the reforms have not really been implemented. Teacher pay is still linked to test scores, and thus the incentive structure to effectuate real change is lacking.

Here, Nussbaum herself waxes pragmatic:

In general, it’s a lot easier to move toward rote learning than to move away from it, since [this kind of progressive education] requires resourcefulness and perception, and it is always easier to follow a formula.

The American education reformers I know would disagree. So powerful is today's false dichotomy between teaching to the test, rote learning, "repetitious exercises and worksheets," and teacher-centered instruction ("bad"), on the one hand, and active problem solving, child-centered instruction, imagination, and creativity ("good"), on the other, that detractors are ignored, thwarted, reprimanded, and, if they happen to work in k12 education, risk being fired for insubordination.

(These are the people, all too readily dismissed in America today, who believe that teaching to the test is perfectly reasonable if the test is a good one, that a certain amount of rote learning and "repetitious exercises and worksheets" are necessary for arithmetic fluency and mastery of algebra [and of phonics and foreign languages], and that teacher-centered instruction is often much more efficient and effective than student-centered instruction.)

Nussbaum, however, seems completely ignorant of America's dissent-crushing education establishment, instead berating Singapore and China for "these authoritarian nations’ fear of true critical freedom." From here, she segues into Singaporean civics education:

In Singapore, nobody even attempts to use the new techniques when teaching about politics and contemporary problems. “Citizenship education” typically takes the form of analyzing a problem, proposing several possible solutions, and then demonstrating how the one chosen by government is the right one for Singapore.

I suspect, however, that Singaporean civics includes more factual information about the functioning of Singaporean political institutions than American civics does. The latest version of American civics, as I discussed two posts ago, does not prepare American students to participate politically as informed citizens.

Nussbaum's worries for American democracy, however, aren't about the diminished content of America's social studies curricula, but about the nefarious influences from across the Pacific:

Singapore and China are terrible models of education for any nation that aspires to remain a pluralistic democracy. They have not succeeded on their own business-oriented terms, and they have energetically suppressed imagination and analysis when it comes to the future of the nation and the tough choices that lie before it.

Nussbaum doesn't entertain the possibility that the U.S. education system might already be achieving precisely these results without help from Singapore and China.

As for "The Ugly Models," the real ugliness is in the stereotype of rote learning in East Asian classrooms for which Nussbaum is but the latest mouthpiece.  As I commented on JoaneJacobs, who wrote about her piece yesterday, it is astonishingly irresponsible and arrogant of Nussbaum, a Professor of Law and Ethics, to make such pejorative comments without actually visiting Chinese and Singaporean classrooms and taking a look at their curricula.

Math problems of the week: riddles in 2nd grade Investigations vs. Singapore Math

More civics and universal preschool: be careful what you wish for!

Two recent segments on NPR remind me of how important it is to qualify carefully what you're calling for--especially when your advice is directed at the education establishment, where phrases--whether it's "conceptual understanding," "higher-level thinking," or "project-based learning"-- are routinely distorted to serve pre-existing agendas.

Two days ago, we hear Sandra Day O'Connor on NPR (on a show whose link I cannot find) lamenting about how little your typical American-born citizen knows about American government. Only one in three Americans, she notes, "can name the three branches."  Inspired by this, she has helped create an interactive website to teach students such things as how a bill becomes a law. She's also calling on schools to spend more time teaching civics.

The problem is that unqualified calls for more civics instruction will further justify the kind of civics that schools currently offer: low-content classes that, having replaced the fact-intensive civics lessons that used to teach students about government, are largely responsible for the kind of ignorance O'Connor is talking about. Exemplified by such top-ranking civics instruction sites as this, this, and this, today's emphasis is on following the rules, picking up trash, recycling recyclables, being a good neighbor, and doing "community service."

In other words, unqualified calls for more civics instruction will make it less likely, not more likely, that students will be able to name the three branches of government.

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Then, yesterday morning, a segment on NPR's Morning Edition reported on Obama's call for universal preschool, citing the French écoles maternelles as an example of how effective universal preschool can be. We hear about French 3-year-olds learning French rhymes and folk songs, eating hot meals, napping in actual beds, and learning to write their names. And then we hear reporter Eleanor Beardsley say "Experts say the focus on cognitive and emotional development at the same time is what makes a good preschool."

But many American preschool programs--in particular, programs like Head Start that are most likely to serve as models for Obama's universal preschools--think they're already doing precisely this. Head Start's mission statement, for example, is:

The early education learning environment, whether in the home or in a school, should provide a rich variety of activities that will foster physical, mental, emotional, and social development.

But there's a distinct difference in both the ingredients and the efficacy of America's Head Start vs. France's écoles maternelles. As E.D. Hirsch explains in The Schools We Need and Why We Don't Have Them (p. 46):

Head Start has not been primarily an academic program. Though momentary academic benefits have sometimes been measured, they are not securely fixed and they quickly fade.

...

Preschool programs elsewhere in the world do achieve long-term academic benefits for disadvantaged students. In France, early schooling permanently boosts educational achievements of low-paid workers and immigrants from North Africa. What, then, makes the academic benefits of early education endure in some countries but fade in our own? A few contrasts: Head Start lasts three hours, is staffed by nonprofessionls, and is nonacademic. The école maternelle (attended by over 90 percent of French three and four-year-olds) lasts all day and goes twelve months a year, is staffed by professionals, and has well-defined academic goals. Children then enter a grade-school system that also has a well-defined academic and cognitive core.

And this core includes, among other things, content-based civics instruction.

Thus, when influential individuals call for more civics and universal preschool, they need to take a close look at what's already out there, imagine how their words may be misinterpreted by those with the power to enact them, and be much more specific about what they have in mind. 

Teaching "because"

In the course of my much-delayed spring cleaning today, I came across these handwritten exercises, one of many that I devised for J about 9 years ago when he was about 5. And I recalled how every night back then, as part of his bedtime routine, I'd present him with pairs of sentences like these and ask him to circle the correct one:

We want to go outside because we open the door.

We open the door because we want to go outside.

It is fall because it is cool outside.

It is cool outside because it is fall.

We go to school because we need to learn things.

We need to learn things because we go to school.

You are dirty because you need to take a bath.

You need to take a bath because you are dirty.

When go on the trip, there are too many bags because you can't sit in the back.

When we go on the trip, you can't sit in the way back because there are too many bags.

You don't drink orange juice because you don't like orange juice.

You don't like orange juice because you don't drink orange juice.

This particular worksheet then segues into why-questions:

Question: Why can't you sit in the back when we go on the trip?

Answer: Because...

Question: Why don't you drink orange juice any more?

Answer: Because...

At the end of this worksheet there's an extended back and forth with written question prompts and blank answer lines which I later filled in with his oral responses:

Question: Why don't you use the second floor bathroom?

Answer: Because I am scared of the second floor toilet.

Question: Why are you scared of the second floor toilet?

Answer: Because earlier the toilet was broken.

Question: Why was the toilet broken earlier?

Answer: Because I broke the toilet.

I can still hear him chuckling as he delivered that last line.

Some people quickly conclude that when an autistic child has trouble grasping the meanings of abstract words like "because," it's because he or she has trouble understanding abstract concepts--e.g., causality. But there's a big difference between conceptualizing and labeling, and in a later post I'll discuss reasons why what looks like a conceptualizing problem is often actually a labeling problem.

As for J in particular, one indication that he didn't have any trouble grasping causality back then was how quickly he figured out which sentences to circle. Another of course, was (is) his mischief-making. One doesn't generally disable toilets to get a reaction from one's parents unless one understands cause and effect.

The age of Technology and Design

Every time a new line of cribs or high chairs is recalled because of loose nuts and bolts or other safety concerns, my first reaction is: haven't people been making these things long enough to know how to make ones that don't fall apart? The problem, of course, isn't that manufacturers yet haven't figured out how to make a safe crib, but that they're constantly trying out new designs to cut costs or look appealing. If it ain't broke, don't fix it just doesn't apply. Instead: the older the appliance, the more likely it is to still be working. One might say the same things about math pedagogy.  

To extend the metaphor between appliances and schools, consider the modern dishwasher. Our three-year-old model has quite the high tech interface: all sorts of buttons for all sorts of options (water temperature; type of dishware), some of which no sane person would ever select (rinse only?  delayed start time???). Open it up, and here's what you see. A detergent compartment whose door no longer opens during the wash cycle; wheels on the lower rack that frequently pop off when you wheel it in or out; silverware holders whose mesh is so coarse that some of our silverware handles extend through it, further impeding the lower rack's wheelability; upper-rack dividers that flop down when anything pushes against them. Layers of grime on the bottom that (so the repairman tells us) require frequent manual mop-up. A machine that (so the repairman tells us) can't handle loose particles larger than grains of rice, such that all dishes must first be "pre-washed"; and, even when we remember to pre-wash every dish, put the narrow-stemmed forks and spoons in upside down, and restrict all large pots to the upper rack so that they don't block the water circulation, still doesn't get the dishes clean enough that we don't have to manually inspect them once they're "done."

While sorting the clean cups from those with cooked-on coffee grounds, orange juice pulp, or milk film, I sometimes find myself contemplating the modern school.  Here we have computers in every classroom, fancy graphing calculators, wireless Internet, and Smart Boards.  But probe deeper, and you find modern math books that ensure neither mastery of the basics nor true mathematical challenge; recent education school graduates whose programs train them neither how to teach math fundamentals to mastery nor how to teach challenging math; and students who increasingly lack fluency in the standard algorithms and facility with geometric proofs and the Quadratic Formula. 

As with the modern dishwasher, the technological frills are in place, but the basic mechanics, the nuts and bolts, are sorely lacking. In this new, right-brain world championed so persistently by Daniel Pink, the Industrial Age has been not enhanced, but supplanted, by the Age of Technology and Design. And thus parents who care about math, like dishwasher users who care about clean dishes, must manually mop up after the machine bleeps "finished."

Math problems of the week: 6th grade Connected Math vs. Singapore Math

I. Final percent problem in Bits and Pieces III: Computing with Decimals and Percents, p. 78:

Explain the general procedures you use to answer these questions about percents. Give specific numerical examples.

a. How do you find the percent equivalent to a given decimal?

b. How do you find what percent one number is of another?

c. How do you find a given percent of a number?

II. Final percent problem in Singapore Math Primary Mathematics 6B, p. 96:

Bridget, Laura and Reagan shared a sum of money. Bridget's share was 40% of the money. Reagan's share was $4 more than Laura's. Laura's share was $16. How much money did they share altogether?

III. Extra Credit:

Which problem involves higher level thinking?